Ratio valuation

DF2-145-I


RATIO VALUATION

Original by professor Javier Vega Fernández of the IE Business School.
Original version, 2 September 2008. Last updated, 26 January 2009.
Edited by the IE Publications Department. María de Molina 13, 28006 – Madrid, Spain.
©2008 IE. Total or partial reproduction of this text is prohibitted without written consent from the IE.



INTRODUCTION
In 1858 the Scottish Egyptologist Henry Rhind bought a papyrus in Luxor, which is currently
known as the Rhind or Ahemes papyrus. The document, which is 6 metres long and more than
3,500 years old, begins with the sentence, “Correct method of reckoning, for grasping the
meaning of things and knowing everything that is, obscurities and all secrets”. It represents the
greatest known source of information about Egyptian mathematics and consists of 87 algebraic
and geometric problems along with their corresponding solutions. Problem 50 asks us to:
“Calculate the area of a circular field whose diameter is 9”.
As far as the author knows, this is the first time that someone has written something related to
the number π, remember that the area of a circumference is π x r2. π (Pi) also calculates the
longitude and diameter of a circumference in the following way:
L
π =

D
So, if we know the longitude (L) of the circumference, we can find out what the diameter (D) is
and vice versa. Experience tells us that 3.1416 is the closest number to π, which means that the
longitude of a circumference, with a known diameter, would be 3.1416 x D and the diameter,
with a known longitude, would be L/3.1416.
Stock market ratios use a system similar to that of the number π, seeking stable relationships
between relevant magnitudes of a company’s accounting - relationships such as profit with cost
and price with the countable units of value.

1. HOW ARE RATIOS USED?

Let’s suppose that we wanted to buy a second-hand flat in a large city. How could we find out if
the price that is being asked is overblown or a bargain? We need a reference point, a standard
that would allow us to compare the price with the flat’s characteristics. In the world of real estate
the standard or ratio par excellence is the price per square metre. If we knew what the ratio was
for all these flats on sale, we would only need to know the surface area that is being analysed in
order to have some notion of a flat’s value.

This generalisation has a problem, not all “square metres” are the same, the location, amenities,
the quality of workmanship make the square metre prices differ. To resolve this problem we
need to group together the “most similar” flats (homes in the same neighbourhood, with a
concierge, with two bathrooms, etc.) so that our ratio may be sufficiently predictable.
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We can do the same with the stock exchange, which is essentially a market of second-hand
shares. If we know the common characteristics of a company’s shares and compare them to
their trading price, we can create standards that will help us value the shares of a specific
company. Obviously, the more similar the company is to those from which we calculated the
ratios, the more reliable will be the estimation we make about the value of the company’s
shares.


2. THE MOST POPULAR RATIO1, PER

PER is the π of finance. It looks at the relationship of a share’s trading with its profit. The best
way to see how it is used is by giving an example. In Chart l we have information about
European electric companies. So, in March 2008 Électricité de France shares had a quotation
of 60.5 euros with an earnings per share (EPS) of 2.92 euros. The PER for this company, Stock
price/EPS, is 20.72 as can be seen in column V of chart l.


Theoretical
Name of company
Country
Quotation
Eps*
PER
Quot/TV
Value
Electricite de France SA
France
60.50
2.92
20.72
55.91
1.082
E.ON AG
Germany
123.33
9.21
13.39
176.36
0.699
Iberdrola S.A.
Spain
9.98
0.58
17.21
11.11
0.899
Enel S.p.A.
Italy
7.10
0.55
12.91
10.53
0.674
Fortum Oyj
Finland
25.88
1.61
16.07
30.83
0.839
VERBUND AG
Austria
47.63
2.41
19.76
46.15
1.032
EDP - Energias de Portugal SA
Portugal
3.87
0.26
14.88
4.98
0.777
Red Electrica de Espana S.A.
Spain
40.92
2.05
19.96
39.25
1.042
ACEA SpA
Italy
12.29
0.73
16.84
13.98
0.879
EDF Energies Nouvelles
France
40.93
1.03
39.74
19.72
2.075
PER sector average
19.15
19.15


CHART I


In this way we can go on to calculate the relationship between the quotation and the EPS for the
European electric companies that range from an exuberant 39.74 for EDF Energies Nouvelles
to a meagre 12.91 for the Italian company Enel.

It is clear that, although the starting point is the same, the PER does not work in the same way
as π. The results of our calculations are too random to establish a reliable rule, but human
beings have always excelled at knowing how to solve these kinds of difficulties and, in this case,
statistics comes to the rescue. Given that there are twelve different numbers relating the electric
companies’ quotations and the EPS, we can use – as the lesser evil – the average of all of them
to establish the value of our ratio. In this case the average is the number that appears at the
bottom of column V, 19.15.

The following step is to apply the PER average to the EPS of the different companies in order to
calculate what would be the theoretical quotation for each of these companies and if they fulfil
the norms for the PER average. The results can be found in column VI. So, if Électricité de

1 Ratio is a latin word adopted by English, and from the English adopted by Spanish. According to the academic Manuel
Seco, an authority on the matter, economists, out of ignorance, relying only on the “o” ending to the word, give the word
masculine gender, el ratio, instead of the feminine la ratio. Many of us have doubted about the convenience of going
with academic orthodoxy over common usage. We have decided to go with the second option but have included this
footnote because we would prefer to be labelled as heterodox as opposed to ignorant.Seco, an authority on the matter,
economists, out of ignorance, relying only on the “o” ending to the word, give the word masculine gender, el ratio,
instead of the feminine la ratio. Many of us have doubted about the convenience of going with academic orthodoxy over
common usage. We have decided to go with the second option but have included this footnote because we would prefer
to be labelled as heterodox as opposed to ignorant.
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France respects the PER average of 19.15, given that its share profit is 2.92 euros, it should
have a value of 55.91, the Theoretical Value (TV) as found in column VI, instead of its current
price of 60.5 (Column III). This means to say that Électricité is extraordinary, it is valued in the
market by some 8.2% over its theoretical value – it is “expensive” in stock exchange jargon –
given that it is valued at 60.5 when it should be valued at 55.91.
On the other hand, Eon AG, if we apply the PER average to its 9.21 earnings per share, has a
theoretical value of 176.36. As the price is 123.33, the share price would be considered “cheap”
or undervalued by almost 30% with relation to the sector average.
And this is all the science there is regarding the PER. Perhaps you are surprised by how
simplistic the reasoning is but in this field, finance, there is not much more to offer, sorry.
Nevertheless, at the end of the chapter we will carry out a more theoretical analysis on ratios,
but for the moment we are going to practise with them.

3. THE “PRICE BOOK” OR RATIO QUOTATION/APPRAISED VALUE (QUOTE/AV)
The Quote/AV compares a share’s price with its appraised value. The example we are now
going to use in order to better understand this ratio is based on the European telephone
companies that appear in Chart II.
I
II
III
IV
V
VI
VII
Appraised value
Quotation / Appraised Theoretical
Name of company
Country
Quotation
Quot/TV
per share
value (PBV)
value
Telefonica S.A.
Spain
18.41
4.22
4.36
15.96
1.154
Vivendi
France
25.81
17.23
1.50
65.16
0.396
Koninklijke KPN N.V.
Holland
12.31
2.44
5.05
9.23
1.334
Hellenic Telecom. Organization S.A.
Greece
18.50
7.48
2.47
28.29
0.654
Portugal Telecom, SGPS, S.A
Portugal
8.25
1.31
6.30
4.95
1.665
Neuf Cegetel
France
35.10
7.09
4.95
26.81
1.309
Telekom Austria AG
Austria
14.35
5.80
2.47
21.94
0.654
Eutelsat Communications Group SA
France
18.10
5.69
3.18
21.52
0.841
Mobistar S.A.
Belgium
55.54
12.13
4.58
45.88
1.211
Elisa Oyj
Finland
19.32
6.53
2.96
24.70
0.782
Price to Book Value sector average
3.78
3.78

CHART II
In March 2008, Telefónica de España was quoted at 18.41 euros and had an appraised value of
4.22 which means that a share was valued at 4.36 times more than its appraised value. If we
calculate the ratio for each one of the companies, we can see that the relationships between the
quotations and the appraised values are very low. Vivendi only values one and a half times its
appraised value and Portugal Telecom values more than six times the total sum of its capital
plus its reserves divided by number of shares. The sector average is 3.78 and if we multiply this
average by the companies’ appraised share values, we will arrive at the shares’ theoretical
values – if these respect the sector average.
Telefónica, with its ostentatious ratio of 4.36, surpasses the average, for which – if we apply this
– the theoretical value would be 15.96. This means to say that the price is 15.4% of the share’s
theoretical value. To sum up, Telefónica is overvalued if we go by the rule of the average. On
the other hand, Telekom Austria’s appraised value is 5.80 euros which, if we multiply it by the
ratio average for the sector, we get a TV of 21.94 euros, far superior to its price of 14.35 euros.

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4. RATIO YIELD PER DIVIDEND OR “DIVIDEND YIELD”
In chart III we can find some of the variables of the most important European motorway building
contractors. Dividend payment is important to this sector and we have calculated the
relationship between the dividend and the share quotation for each company. The average, at
the bottom of column V is 3.10%, which means that this is the average profit per dividend for the
sector.

I
II
III
IV
V
VI
VII
Dividend per
Dividend
Theoretical
Name of company
Country
Quotation
Quot/TV
share
yield
Value
Societe des Autoroutes Paris-Rhin-Rhone
France
73.30
2.83
3.86%
91.36
0.80
Brisa - Auto-Estradas de Portugal SA
Portugal
9.85
0.31
3.15%
10.01
0.98
Obrascon Huarte Lain S.A.
Spain
22.45
0.38
1.69%
12.27
1.83
Societa Iniziative Autostradali e Servi
Italy
9.24
0.30
3.25%
9.68
0.95
Autostrada Torino-Milano SpA
Italy
12.64
0.52
4.11%
16.79
0.75
Itinere Infraestructuras SA
Spain
7.13
0.18
2.52%
5.81
1.23
Dividend yield sector average
3.10%
0.031

CHART III
If we now divide2 the dividends by the average profit, we should get the capitalisation, which is
to say by discounting an infinite number of dividends, a figure of 3.1% - the theoretical value of
each share. For example, Societé des Autoroutes has a theoretical value of:

This means to say that this company, with the dividends that it pays and the profitability of the
sector dividend, should be valued at 91.36€, or likewise, the company is undervalued by 20%
with these determining factors. On the other hand, the low dividends that Itinere pays make its
theoretical value only 5.81 - 23% below its price.

5. ENTERPRISE VALUE EBITDA OR THE RELATIONSHIP BETWEEN SHARE
VALUE AND MARGIN
We are now going to work with a ratio that has slightly more complicated variables. In finance,
Enterprise Value is a recent concept that values shares in function of the debt market. Imagine
that we have a company with a balance sheet like the one given below.
Assets
Debt to Contable Value
Debt to Market Value
Cash
100
Debt
700
700
Net current asset
500
Capital
900
1,400
Fixed assets
1,000
1,600
1,600
2,100


2 This ratio is a little different from the previous ones. As we have seen with the PER as with the P/BV we get a figure
that we multiply by the variable in question: the PER times the EPS and the P/BV times the countable value. This is why
these ratios are called multiples or multipliers.
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Now we must find out what the market value of the debts are by adding the market
capitalisation of the shares to the market value of the debt. So, if the total value of the shares is,
shall we say, 1,400 and the debt market value is 700, in this example as in the nominal value,
the market value of all the debts would be 2,100 – as indicated in the shaded column – which is
500 above the appraised value.
But if the debts have a market value of 2,100, then the market is valuing the assets at this same
quantity, which means that the debts certify that the assets value 500 more than their appraised
value.
On the other hand, the EBITDA, (Earnings Before, Interest, Tax, Depreciation and Amortization)
is an intermediary result of the result account or a kind of operative margin. Let’s now look at
how it is applied.
I
II
III
IV
V
VI
VII
VIII
Theoretical
Name of company
Capitalization
Debt
EV
EBITDA
EV/EBITDA
Quot/TV
Value
Exxon Mobil Corporation
452,130.81
9,566.00
461,696.81
93,663.94
4.93
537,083.61
0.84
Chevron Corporation
182,332.52
7,232.00
189,564.52
43,820.52
4.33
248,517.12
0.73
ConocoPhillips
125,139.12
21,687.00
146,826.12
38,493.88
3.81
202,974.32
0.62
Occidental Petroleum Corporation
62,070.91
1,788.00
63,858.91
12,741.93
5.01
72,577.56
0.86
BP plc
100,824.77
31,045.00
131,869.77
42,951.95
3.07
219,634.90
0.46
Repsol YPF S.A.
25,870.10
7,948.00
33,818.10
8,625.36
3.92
42,392.07
0.61
Royal Dutch Shell plc
109,500.04
18,099.00
127,599.04
52,161.50
2.45
286,330.47
0.38
Indian Oil Corporation Limited
614,841.63
294,811.19
909,652.82
126,449.33
7.19
443,183.36
1.39
CNOOC Limited
530,668.88
20,341.83
551,010.71
51,102.17
10.78
277,905.09
1.91
Hellenic Petroleum S.A.
2,726.21
1,189.10
3,915.31
480.95
8.14
1,617.86
1.69
PetroChina Company Limited
2,020,904.75
71,397.00
2,092,301.75
277,486.84
7.54
1,548,095.76
1.31
Petroleo Brasileiro S.A.
418,435.72
38,307.82
456,743.54
51,552.66
8.86
262,568.29
1.59
EV/EBITDA sector average
5.84
5.84

CHART VI
In chart IV we have data on the most important petroleum companies; the EV, in the fourth
column, is a sum of the market value of the debt and the shares. The Ebitda is in the fifth
column and the EV/EBITDA ratios and averages are in the sixth.
If we now multiply each company’s Ebitda by the ratio average, we will get the Enterprise Value
for each company and if we subtract the debt value from this we will get the theoretical value of
the capital which is what you can find in column VII. Hence, Exxon, which has a lower than
average EV/EBITDA, should have a theoretical value superior to its market capitalisation. On
the contrary, Petróleo Brasileiro, which has a ratio superior to the average, will have a
theoretical value inferior to its market value.


6. THE RELATIONSHIP BETWEEN PER AND GROWTH, THE PEG RATIO

If we recall the model called Gordon-Shapiro, we can say that a share’s quotation is related to
dividends, the cost of equity (CE) and the growth forecast (g) for these dividends in the following
way:


If we now divide the two equal figures by the earnings per share we get the following:

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What this tells us is that the PER – given that profits and dividends at moment zero of the
valuation are known - depends on the cost of equity and growth forecasts and the smaller the
difference is between these two magnitudes , the greater the PER will be and vice versa. It also
means that for similar discount fees the PER will be greater for those shares that have the best
outlook.
The PEG ratio, or PER growth, arises from this rationale. Companies with the highest growth
forecast will have a greater PER and accordingly, those with the lowest; will have a lower
growth forecast.
In chart V we have information about companies that manufacture communication systems. In
columns II, III and IV we have the quotation, the EPS and the PER and in the V the annual EPS
growth predicted by analysts.
If we now divide the PER by the growth, not by percentage but by number, in other words not by
.0581 in the case of Cisco, but by 5.81, we get the number of PER points provided by each
growth point.

I
II
III
IV
V
VI
VII
VIII
IX
Theoretical
Theoretical
Name of company
Quotation
Eps
PER
∆ (%)
PER
Quot/TV
growth
PER
Value
Cisco Systems, Inc.
23.94
1.52
15.76
5.81
2.711
10.91
16.58
0.69
Nokia Corporation (ADR)
33.80
2.50
13.53
2.19
6.165
4.12
10.30
0.30
Nokia Oyj
22.22
1.73
12.81
11.39
1.124
21.39
37.11
1.67
Research In Motion Limited
97.00
2.21
43.96
31.27
1.406
58.73
129.58
1.34
Research In Motion Limited (USA)
97.92
2.24
43.71
30.13
1.451
56.58
126.75
1.29
Juniper Networks, Inc.
25.83
1.13
22.88
11.40
2.007
21.40
24.16
0.94
Harris Corporation
47.85
3.44
13.93
15.73
0.885
29.54
101.48
2.12
TomTom NV
29.51
2.79
10.58
29.56
0.358
55.50
154.81
5.25
Nexans
72.76
7.57
9.61
6.86
1.400
12.89
97.60
1.34
NDS Group plc (ADR)
49.38
2.69
18.33
14.43
1.270
27.09
72.99
1.48
PER growth average
1.878
1.878

CHART V

In Cisco’s case, each forecasted growth point provides 2.711 PER points and in Nokia’s case,
6.166. If we calculate the average of all PEG, we can say that in this sector, each point of
growth provides 1.878 PER points, which means that if we follow the average, Cisco should
have a PER of 1.878 x 5.81 = 10.9. With this theoretical PER, the share’s theoretical value
would be 16.68, 69% of its price.

Up to now our intention has been to explore how ratios are used by financial analysts. We are
presently going to continue with the theoretical foundations on which ratios are based and their
synthesis for valuing shares by the discounted cash flow method.


7. RATIO VALUATION AND DISCOUNTED CASH FLOW VALUATION. A
FUTILE CONTROVERSY

My suffering students in Corporate, who would give their lives to work in mergers and
acquisitions so that they could buy a Porsche before turning 30, return from job interviews
disappointed when the prospective employers tell them that no matter how much they may have
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learnt about company valuation by discounted cash flow, only ratio valuation counts on the
market.
The tendency of investment bankers to use IRR and ratios is a mystery for me and an even
greater mystery is their hostility to using discounted cash flow models. Perhaps out of lack of
awareness that both discounted cash flow and ratios are the same models.
If you remember, when we studied business valuation by discounted cash flow (DCF), we did
and exercise about quantifying the business plan to establish how much we were going to sell,
how much it was going to cost us, how much we were going to charge and pay, etc. Our aim
was to find out how much money the company was going to make each year in order to
calculate its current value.
Normally, we estimate five years of Free Cash Flow and then calculate a residual value (RV) for
infinite future flows. Do you remember how we calculated this? We made suppositions about
future growth from the last Cash Flow and applied the capitalisation with growth formula, so
that:



But this final figure looks like a ratio, doesn’t it? If we separate (1+g)/(r-g) we are going to get a
number that multiplies to the CF, in other words a multiplier. Let’s look at an example, imagine
that the discount rate is 10% and growth is 4%. This means that:




This leads us to conclude that the multiple that turns the Cash Flow for year n into an RV is, at
10% capital cost and 4% growth, 17.33.
We can even make up a list of ratios that could be called “Price, CF, discount rate, growth rate
or rather, “PCFg”, as appears in chart VI:

CF multiplier for different combinations of r and g
WACC
8.0%
9.0%
10.0%
11.0%
12.0%
g
2.0%
17.00
14.57
12.75
11.33
10.20
2.5%
18.64
15.77
13.67
12.06
10.79
3.0%
20.60
17.17
14.71
12.88
11.44
3.5%
23.00
18.82
15.92
13.80
12.18
4.0%
26.00
20.80
17.33
14.86
13.00
CHART VI

The combination r=10; g=4%, gives us a multiplier of CFL of 17.33. The greatest multiplier will
be that which has the least difference between r and g, which is to say the combination of 8%
and 4%. The lowest multiplier will be that which has the greatest difference, 12% and 2%.

Surprisingly, we are using ratios in the DCF valuation. The same will happen the other way
round, meaning, do we us the discount when valuing by ratios? Let’s find out.
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As we have already seen, the PER is used as an instrument to predict the value of a company
in the following way:

Value of the analysed company = Earnings x Sector average PER

On the other hand, we can also say the opposite of the PER is:

1
Eps
=

PER
Quotation

This is the profitability, in so far as the investment made in a share with respect to the earnings
that are obtained, which is the same as what the shareholders have earned by investing in this
share in this particular year. If we connect these two lines of reasoning, we can say:

earnings
earnings
Value of analysed company =
=

1
average profitability
PER average

This is nothing more than the discount or update on the earnings per share to the sector
average profitability rate, or the discount of infinite future earnings equal to those which the
company currently obtains.
Well it seems that we use ratios in the discount and discounts in the ratios or likewise that
ratios and discounts are the same thing. To discount is to expand the ratio valuation and ratio
valuation is to condense the DCF model.
We have an example of how unconsciously ratios stand up to the discount model in the
valuation of “dotcoms”. Amid the mushrooming of internet companies, analysts made a big
effort to value these companies which, as Damodaran said, “have no history, no comparables
and no earnings”.
In a Salomon Smith Barney report from 19993, Yahoo! were valued by a novel method, the
discounted PER. There is a summary of this analysis in Chart VII:

Current value of the PER obtained future value


Discounted (Discounted P/E)


Yahoo!
1998
2003



Publicity market in the USA (millions of dollars)
200,000
258,000
Internet share
1%
7%
Yahoo! share in the internet market
15%
20%
Yahoo! sales (millions of dollars)
300
3,612
Yahoo! net margin (in percent)
25%
35%
Yahoo! net margin (in millions of dollars)
75
1,264.2
PER of 50, Value in 2003 is (in millions of dollars)

63,210
PER of 70, Value in 2003 is (in millions of dollars)

88,494
The Value at the end of 1998 of 63,210 million at 20%

30,483
The Value at the end of 1998 of 88,494 at 15%

50,596
The Average value is

40,539
The Market Value at the end of 1998 was

44,000
CHART VII

3 Hamel y Andersen. (1999) “Internet Valuation”. Salomon Smith Barney. Global Equity Research.
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This method consists in estimating what the PER will be within five years for a currently
emerging company that has a growth potential superior to that of conventional companies. To
do this, analysts made the following hypothesis:

The publicity market grew 5.2% from the year 1999 to 2003. In the year 1999 internet publicity
accounted for 1% of the market and reached 7% five years later.

Yahoo! had a 15% share of this 1% but its position in the market allowed it to increase its share
to 20% in this period. In short, if at that moment Yahoo! publicity sales were 300 million dollars
(200,000 x 1% x 15%) the expansion would set them at 3,612 million in 2003. Bearing in mind
that the percentage of earnings would be 35%, the net earnings would reach 1,264 million.

A PER would have to be applied to these earnings, bearing in mind that in 1999 companies
such as Microsoft (62) Cisco (109) and Dell (66) could be figured at between 50 and 70. At
these PERs, Yahoo!’s value in 2003 would be between 63,210 and 88,494 million.

These future values have corresponding current values if we discount at the appropriate rate.
Van Hamel and Andersen believed that this could be between 15 and 20%. By discounting the
lowest future value from the highest future value and the highest future value from the lowest
one we can arrive at the valuation limits which would have a range from between thirty and fifty
thousand million dollars. The average of these two figures would be 40,539 million. If we add
cash and European investments to this figure, we get a value near the market capitalisation of
Yahoo!, which would be 44,000 million.
Van Hamel y Andersen said with respect to this valuation procedure that:

“There is little doubt that the discounted PER methodology leaves much to be
desired. Nevertheless, it’s good sense, versatility and user-friendliness make it very
practical for a sector as volatile as the Internet”

And they immediately after added to this:

“To avoid criticising all these expensive post-graduate MBA and CFA programmes
and, in part to maintain pride in this uncharted territory, financial analysts got used to
employing a discounted cash flow valuation. Although we subscribe to the theory
that discounted cash flow valuation provides us with the most thorough analysis of a
company and its business plan including aspects such as variations in the operative
margin and financial needs. The truth is that many of the assumptions applied in
creating a model for Internet company valuations are, in most cases, conjectures.”
(…) “Nevertheless, despite these inconveniences, it is very seldom that we make a
valuation without using the Discounted Cash Flow model.”

We would have to say that the analysts are right with regards to one thing, that the assumptions
are conjectures. That is the way it is, but not much more than the assumptions made while
using the discounted PER model, please see Chart VII. This means that we can say there are
companies that cannot be valued because of their volatility but not that we use the simplest
method because these companies are valueless. This is called a waiver. We also have to draw
attention to the fact that despite the difficulties, the Cash Flow method is always or almost
always used.
In short, there are not two kinds of valuation methodologies, there is only one – that of the
discounted future earnings, which in each case means making conjectures. The debate should
be focussed on whether it is necessary to examine the company’s business plan, making
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hypothesis about what is going to be sold; how much what it is going to be sold will cost; how
much is going to be charged and paid; how much money will be asked for from the banks and
shareholders, etc. This allows us to find out what the company’s strategy is for the next few
years.

If we are only using ratios, the result that we get is how much a company is worth if it behaves
like its average counterparts yet there are things that the average tells us but many more that it
hides. So, wouldn’t it be better to value using the Discounted Cash flow and then later
comparing that with the sector average? This comprehensive view seems more reasonable and
is generally the most used.


8. RATIOS AND THEIR HISTORY

Finance, as explained in another part of this text, is as old as civilisation itself. Some of the
ratios that we assiduously use come from very far back. Others are more recent and come from
tools used in accounting and the needs of financial analysis.
As far as the author knows, PER was already being used in the Roman Empire. In a paragraph
of “De beneficiis” by Seneca we can read:
“There is no one, upon having decided to buy the Tusculano and Triburtino gardens
by judging them to be important for his health and for spending summers, who then
considers how many years’ purchase he gives for it.”

The cost and yield is the Tusculano gardens’ relationship of price/earnings. It is that way to such
a degree that translators of Seneca to English translated the sentence as “consider how many
years` purchase he gives for it”.
The phrase “Number of Years´ Purchase” is of medieval origin, probably from the 12th century.
This is what we now call “payback” or the period of time for getting back one’s initial investment
and it is also the PER, which is sometimes defined as the number of years it takes to get back
one’s initial investment via yield.
In epigraph 6 of this chapter, we discussed the meaning of the inverse of the PER. We shall
now look at how this inverse PER was used during the times of the classic economists. In 16904
John Locke said:
“One should expect that the interest rate would be the average value of land in function of
the value of the annual yield. If the earnings were 100 pounds annually and this was
perpetual, the land’s value would be as follows:
• 1,000 pounds if the interest rate were at 10%
• 1,250 pounds if the interest rate were at 8%
• 1,666 pounds if the interest rate were at 6%
• 2,000 pounds if the interest rate were at 5%
• 2,500 if the interest rate were at 4%”

This is to say that the land’s value, with a fixed yield, is logically inversely proportional to the
market interest rate. No one is going to pay more than 1,000 for an income of 100 if he can
invest this thousand at 10%.
But John Locke went even further – basing the value of the land on its capitalisation and the
total sum of its earnings – he came up with a ratio which is as follows:

4 I beg of you to reflect on this paragraph by John Locke for 10 minutes because in it is contained the essence of
finance.
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“We can conclude that land should be sold in proportion to its usefulness in accordance
with the following rates:
• When price of money is at 10%, for 10 years of yield
• When the price of money is at 8%, for 12 1/2 years of yield
• When the price of money is at 6%, for 16 2/3 years of yield
• When the price of money is at 5%, for 20 years of yield
• When the price of money is at 4%, for 25 years of yield”
In short, when the interest rate is at 5%, the land’s value - with a capitalisation on a fixed yield of
100 - is 2,000. If we compare this 2,000 with the yield of 100, it means that we need 20 years of
earnings to recoup the cost of the land. This ratio is what is called “Number of Years’ Purchase”
and it is the predecessor to our mega famous PER.
Nevertheless, at the beginning of the 20th century the PER ratio did not enjoy much prestige, its
inverse was more frequently used, which is to say the capitalisation on profit. The debate
focussed on finding an appropriate rate to discount the profits from companies. Since the great
crash of ’29, the PER naturally intervened in the markets and today continues to reign among
those who prefer taking shortcuts when valuing companies.
The Price/Book ratio has its predecessor in “par value” or face value or the value which one
would have to pay when buying a share directly from the company issuing the share. In the
incipient American stock market of the middle of the 19th century, an effective means for
valuing shares was needed and no better one was found than that of using the value that was
stamped on the very same shares. Experts later began to think that as business developed,
companies made (or lost) money and this affected their share value. And from this came the
Price/Book which compared a share’s price with its appraised value comprised of capital plus
reserves.
The ratio of profitability per dividend also comes from the heroic times of the end of the 19th
century. Investors compared shares with bonds and the profit potential of the two, dividends and
interest. In short, “dividend yield” was useful for comparing the profitability of a share with that of
a bond according to interest without analysing the risk in great detail.
EV/Ebitda is a ratio derived from the incomprehensible success of Ebitda. Ebitda went on to
become the mother of all intermediary measurements of a balance sheet during the eighties of
the last century because of an increase in purchasing operations with extreme debt (LBO)5 It
seemed like Ebitda would avoid all the problems brought on by the EBIT and BDI, with respect
to the money the company really made, because of the simple fact that it was the quantity that
would serve to fulfil the debt payment – both interests and capital. Today it is the ratio most
appreciated by the financial community, above all by Private Equity6 funds.
Finally, PEG is a modern ratio, created in 1997 by the heterodox financial managers, “The
Motley Fool” and very tied to the high growth rate of the economy during that time.




5 Leverage Buy Out, translated into Spanish as “compras apalancadas”.
6 On 15 Octuber, 1992, while the financial market was being revamped, the following article appeared in the newspaper
“Expansión”: “AB Asesores y HSBC valoran al Atlético de Madrid entre 60.000 y 70.000 millones de pesetas.” (AB
Asesores and HSBC value the Spanish football team Atlético de Madrid at between 60,000 and 70,000 pesetas).
Further on in the article a spokesperson clarified: “The valuation method on which the calculation was based is called
enter-price valium. This is a wonderful example of the cultural circumstances of the period. The following day AB
Asesores denied having taken part in any valuation.
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9. PRECAUTION WITH RATIOS
We have seen that the PER is a multiplier of a company’s earnings used to calculate what the
company’s value is. And evidently, the more adjusted the earnings are, the more representative
the value we get from this calculation will be.
To use the PER we need to use adjusted earnings yield, which is what best represents what the
forecasted future earnings of the company might be. We must eliminate from it all that might be
unusual such as extraordinary earnings or losses.
Obviously the PER cannot be used when there are losses.
Each country has its own accounting system: during the eighties of the last century the PER of
the Japanese stock exchange almost doubled that of the United States stock exchange – due to
conservative Japanese accounting practices with reference to depreciation and precautionary
measures, their earnings were reduced compared to the Americans. When earnings were
adjusted, the PER results of both markets were more similar.
If you have to be careful with the after-tax earnings yield to calculate value using P/E, you have
to be even more careful in reference to Ebitad, according to the recommendations of the
Security Exchange Commission (SEC).7
“When evaluating the Evitad, investors must be aware that it cannot be considered
alone but along with other factors that can influence operations and investments, such
as: changes in the operative needs of the funds, property and building purchases. It is
not a measure of yield in accordance with the generally accepted accounting criteria, it
is neither an alternative nor substitute for the EBIT, the operating margins nor the Free
Cash Flow and it must not be used as an indicator of a company’s operative yield or as
a measure of a company’s liquidity.”
With this simple paragraph the SEC is saying that the investment needs, the operative cash
needs and the investments in property and buildings of two companies are different, the
EBITDA of these two companies will not be comparable.
The Price/Book ratio seems not to include the discount, but in fact does. We can demonstrate
so - but believe me it is not worth it – for a company with zero growth:

ROE being profitability over appraised value:

What this means to say is that the price of a share cannot be greater than its appraised value if
the ROE is not greater than the cost of the equity.
If we clarify the contribution of this formula, we get:


7 This is the United States financial market regulator.
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This is a good ratio for valuing companies where the tangible assets generate earnings. An
example is banks, where loans and volume of shares are what generate income.

Profitability per dividend is a ratio that is used to value dealerships because the dividend is the
money left over after paying banks and making investments in maintenance. These companies
do not consider reinvesting in Equity Cash Flows because there are none.
With other kinds of companies care must be taken with this ratio since the dividend may be
based on a “dividend policy” and not coincide with the money left over after investments and
meeting debts. What also might occur is that the company, instead of paying dividends, may be
buying back shares, with which the dividend is cancelled.

With reference to the PEG, the very inventors of this say that it is not applicable to sectors such
as airlines, banks, securities firms, leasing companies, petroleum drilling companies and estate
agents. What is more, it is only applicable to small and medium-sized companies.

It is logical that a system so practical and easy to use would have a lot of limitations and
precaution must be taken when using it.



10. CONCLUSIONS

Ratios are a summary of valuation by discounted cash flows. They are very easy to use, they
are calculated for comparable companies; the average is calculated and applied to companies
that we want to value. We have explained the most popular ones on the market, but although
there are many others, all of them go by the same rules of use.

The simplicity with which we can apply ratios makes them a slave to their limitations. We believe
that they must be used with care and as a compliment to the discounted cash flow valuation
which is what specifies what can be expected of a company that is the aim of a valuation.

We shall finish with an image of the house Fallingwater by the architect Frank Lloyd Wright. If
you analyse a company only using ratios or only using the company’s cash flow, what you will
see is something like figure 1. If you analyse using both ratios and discounted cash flows, what
you will see is what appears in figure 2. So, you decide.


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Figure 1
Figure 2


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